Project Summary Over the past decade, it has become clear that mixture between diverged populations (admixture) has been a recurrent feature in human evolution. It has also become evident that a detailed un- derstanding of admixture is essential for e ective disease gene mapping as well as evolutionary inference. Nevertheless, adequate analytical tools to dissect admixture and its impact on pheno- type are lacking. As a result, disease gene mapping or evolutionary studies have either excluded admixed populations or relied on simpli ed models at the risk of inaccurate inferences. This pro- posal proposes to develop computational methods to infer the genomic structure and history of admixed populations across a range of evolutionary time scales and to lever- age this structure to obtain a comprehensive understanding of the genetic architecture and evolution of complex phenotypes. The proposed methods will integrate power- ful sources of information from ancient DNA with genomes from present-day human populations. These methods will enable populations with a history of admixture to be studied just as e ectively as homogeneous populations. The rst step in obtaining a thorough understanding of admixture is a principled and scalable statis- tical framework to infer ne-scale genomic structure (local ancestry) and evolutionary relationships. This proposal leverages recent advances in statistical machine learning to develop e ective tools for the increasingly common and challenging problem of local ancestry inference where reference genomes for ancestral populations are unavailable (de-novo local ancestry). Further, the proposal intends to develop models to infer complex evolutionary histories as well as realistic mating patterns in admixed populations. These inferences will form the starting point to systematically understand how admixture has shaped phenotypes. For example, it is becoming clear that admixture between modern humans and archaic humans (Neanderthals and Denisovans) could have had a major im- pact on human phenotypes. This question will be explored by applying novel statistical methods to large genetic datasets with phenotypic measurements to assess the adaptive as well as phenotypic impact of Neanderthal alleles. Finally, large collections of genomes from extinct populations that are now becoming available due to advances in ancient DNA technologies can lead to vastly more powerful methods for evolutionary inference that overcome the limitation of methods that rely only on extant genomes. Statistical models that use ancient genome time-series to eciently infer admixture histories, local ancestry and selection will be developed.